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GAZA CITY (CNN) -- About 1.3 million Palestinians are heading to the polls Wednesday in the first parliamentary elections in a decade -- a key vote that observers say could be pivotal in the Palestinian push for statehood.

On the eve of the election, Palestinian leader Mahmoud Abbas urged Palestinians to turn out for the vote, and an array of militant groups said they would not disrupt voting, which will be held at more than 1,000 polling stations. The polls opened at 7 a.m. (midnight ET) and will close at 7 p.m. (noon ET).

"Voting is the right of every citizen," Abbas said. "It's a national obligation because the results of the election should reflect a truthful expression of all Palestinians."

At issue in the balloting is the political battle between Abbas' ruling Fatah Party and Hamas, the militant Islamic group that has called for the destruction of Israel and is considered a terrorist group by the U.S. State Department.

Hamas is also known to Palestinians for providing a network of social services.

It has capitalized on widespread dissatisfaction with what is seen as corruption within the Palestinian Authority and Fatah, and a perceived inability by the authority to manage the affairs of the Palestinians.

Hamas, which boycotted the last election in 1996, could win at least one-third of the 132 seats in the Palestinian Legislative Council, according to pollsters, with that support appearing to have grown in the final days of campaigning.

Samar Assad, the executive director of the Washington-based Palestine Center, said she believed Fatah needed more than 55 percent of the vote to "reclaim its credibility and its historic mandate."

"It does not look like it's going to get that," she said. "Either way, this is a win-win situation for the Palestinian people, because all groups running in this election ... will really have to work hard to gain the trust and get the legitimacy from the Palestinian people."

She added, "It's going to be a tight race between Fatah and Hamas."

Acting Israeli Prime Minster Ehud Olmert had a message Tuesday for Palestinians just hours before the start of the election, issuing a thinly veiled plea that they not elect Hamas to run the next Palestinian government.

"Do not choose extremists who have led them from tragedy to tragedy and to misery," he said. (Full story)

Abbas is hoping Hamas will be tamed by mainstream politics, that the day-to-day duties of government -- such as running schools, hospitals and garbage collection -- will lead to pragmatic change within the group.

"Hamas must understand these elections are the way to one authority, one legal gun and the rule of law," said chief Palestinian negotiator Saeb Erakat, a Fatah member.

Israelis skeptical

Some Israelis, however, remain skeptical of that possibility.

"I think that Israel is very concerned that Hamas, once in power, begins to feed itself up and form the basis for a militant Islamic threat against Israel that we have never known before," said Dore Gold, with the Jerusalem Center for Public Affairs.

"It simply doesn't work when you have a committed ideological movement like Hamas, which in addition has religious motivation. They can't be tamed by garbage collection."

Thousands of Palestinian police have fanned out across the West Bank and Gaza to protect voters from any possible violence during the election.

More than 17,000 local election officials will work during the voting, along with hundreds of international observers, led by former U.S. President Jimmy Carter.

More than 1.3 million voters are registered, with more than 120,000 eligible voters in East Jerusalem, which is under Israeli control but mostly populated by Arab Palestinians.

Israel's Cabinet earlier this month unanimously approved a proposal allowing Palestinian residents to vote at polling places in East Jerusalem. But the Cabinet said Hamas would not be allowed to campaign there. (Full story)

In one violent act Tuesday, gunmen with the Al Aqsa Martyrs Brigades, a militant offshoot of Fatah, killed one of their own, slaying a leading Fatah politician, Abu Ahmed Hassouna, in the West Bank city of Nablus.

In Washington, U.S. State Department spokesman Sean McCormack on Tuesday refused to comment on reports that Hamas leaders have said they are willing to take lower-level ministry posts and leave the more political ones to Fatah.

"We'll wait to see how the elections turn out and what government emerges as a result of these elections," he said.

He added, "It's only logical that in order to move forward on a process where the Palestinians realize a state, that you have to have a negotiating partner that is committed to negotiating in an atmosphere free from violence and that renounces the idea that it wants to eliminate the existence of the party sitting across the table."